Do you start fine tuning the system with cables or tubes ?

Yes, assumption is that both the cables and tubes are already quite good. That's why I called it fine tuning, your system is tuned but you want to take it a little higher without changing active components.

In my case, cables are excellent and I don't think about upgrading them because it would make more sense to upgrade analogue front end and speakers before doing it. So I proceed with tubes, though here too I believe I have found the right balance for my VAC Avatar SE integrated. One could do better but at high cost.

Neither. Your system should sound good with stock tubes and basic, well  designed cables. If something doesn't sound right, fix the problem. Using tubes and cables to fix a problem is almost always a bad idea. Once you get everything sounding OK, different tubes an cables can be used to enhance an already good sounding system.

In my modest but very revealing system I started with the entry level cables I had (Zu ) . I rolled tubes in my pre and power amp. I went to Anti-Cables and rolled tubes again. I then went to Morrow level 5 and rolled again. Please keep in mind that almost ALL of the tubes were purchased in the beginning. Also @hilde45 pointed out room treatments are paramount. Part of my tube rolling was to accommodate for room acoustics, which would be unnecessary if my room was treated properly in the first place. Happy Listening, Mike B. 

I have found that cables have a much bigger effect than tubes if you are using good cables.  Changing cables is often as dramatic as change components if you are using good cables.  I've found that changing tubes is much more subtle than changing components or changing cables.

Good cables typically cost at least 10 times as much as good tubes, and the differential is usually much more than that so it's not surprising that cables make a much bigger difference.

This is interesting. Some say that after a certain level tubes make bigger difference while others say the opposite. In terms of cost it can vary wildly. If you buy used cables then even excellent ones while still expensive are not terribly bad. Tubes, well, it depends, right ? Also on how many of them you need.